#### Vol. 3, No. 4, 2008

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Scientific Advantage Submission Guidelines Submission Form Ethics Statement ISSN: 1559-3959 Author Index To Appear Other MSP Journals
Effects of layer stacking order on the $V_{50}$ velocity of a two-layered hybrid armor system

### Pankaj Kumar Porwal and Stuart Leigh Phoenix

Vol. 3 (2008), No. 4, 627–639
##### Abstract

We develop a theoretical and computational model to investigate the ballistic response of a hybrid two-layered flexible armor system. In particular, we study the effects of stacking order of the two fibrous layers, which have distinctly different mechanical properties, on the ${V}_{50}$ limit velocity. A system consisting of Kevlar and Spectra fabrics is studied in detail. For this system, previous experimental results of Cunniff show nearly a factor of two difference in the ${V}_{50}$ velocities for the two possible stacking orders. The new model presented here extends our previous multilayer model by directly addressing interference effects between the two layers, treated here using length and tension compatibility along the radial direction away from the projectile. The primary task is to calculate strains in the individual layers in the presence of constraining interference that forces the nested layers to have a common impact cone shape different from what would be generated by the impact if the layers were allowed to deform freely. We show that this interference, together with relative areal densities of the layers, have a significant effect on the strain evolution in the layers, particularly near the edge of the projectile where failure initiates. As observed experimentally by Cunniff, our model predicts a large decrease in the ${V}_{50}$ velocity of the hybrid armor system when Spectra is the strike layer. However, to achieve this reduction it is necessary to use a lowered normalization velocity in multilayered Spectra systems than the theoretical value obtained from basic fiber properties. Besides matching the experimental results of Cunniff, the model reveals many subtle transitions in the onset and effects of interference between the layers. Somewhat surprising and contrary to conventional wisdom is the observation that layer interference can sometimes be beneficial depending on the relative mechanical properties and areal densities of the two layers.

##### Keywords
multilayered hybrid armor systems, stacking order, thermal effects, layer interference, $V_{50}$ velocity, impact velocity versus residual velocity